Knoppix up to the version 5 series did what you want and did it very well. The Knoppix 6 series won't. I have not seen an explanation of why, only some speculation. The implication is that people will install to USB and then they can have persistent store.

There is an unofficial cheat code that could help but you would have to remaster your CD in order to try it and you probably are not prepared to go that far.

The Wiki is very much out of date. It has almost no information on Knoppix 6. I don't know who should or could maintain this but it isn't the developper(s) of Knoppix. It is probably the likes of the Senior Members on this forum.

It is interesting to learn that CD-with-persistence does not work on Ubuntu or Debian either. It is also interesting that Knoppix was your third choice.

It seems the Wikipedia is out of date when it still describes the old, glorious, Knoppix capabilities. The Wikipedia entry on Klaus Knopper is more up to date when it describes Knoppix today as:

Therefore "a well-known live CD Linux distribution" may not be entirely appropriate.
Alas, poor Klaus !

You might try Puppy Linux. It is a few years since I used it and I think the creator has stepped down. Puppy might still allow persistence even with the CD. You might not find it a good teaching vehicle and it certainly won't have the same huge choice of software packages.